Maxwell's Equations Broken Down

Heaviside modified Maxwell's equations to provide a set of equations that define much of electromagnetism as we know it today.

The Maxwell-Gauss' equation for electric fields defines electric fields as a vector field pointing from positive to negative.

The Maxwell-Gauss' equation for magnetism is nothing but a vector calculus identity. If the magnetic field is just a curling electron field then the divergence of a curl will always be zero.

Defining the magnetic field is done through the Maxwell-Ampere equation. The current is the curl on the magnetic field. Stated more simply a localized electron flow will create local and more distant electron turbulence. Due to constructive or destructive electron turbulence conductors will either attract each other or repel each other.

The Maxwell-Ampere equation apply with the curl of a magnetic field is proportional to the currents. If a current field is curled then a proportional magnetic field will be the result. This allows us to build a coil and observe a magnetic field. Really all that is observed is a curling electron field. The additive electron field created by the coil maximizes magnetic effects.

The last effect that Maxwell and Heaviside observed is known as the Maxwell-Faraday equation. This equation largely describes conservation of angular momentum using vector calculus. When a group of electrons enters a region where there is tight spin of electrons the introduced electrons spin tightly. Due to the conservation of angular momentum a very broad spin of electrons sets up in opposition to the tight spinning electron field.

Coils take advantage of the broad spin with each end of the coil catching a momentum effect from a moving coil. We call the Faraday momentum of electrons the electromotive force.